Answer:
[tex]y<-\frac{3x}{2}+1[/tex]
Step-by-step explanation:
The straight line passes through (0,1) and (2,-2).
Equation of a straight line passing through two points (x1,y1) and (x2,y2)
is given by:
[tex]y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})[/tex]
[tex]y-1=\frac{-2-1}{2-0}(x-0)[/tex]
[tex]y=-\frac{3}{2}x+1[/tex]
Everything to the left of the line is shaded.
We have to visualize the graph:the straight line has a positive y-intercept and a negative slope.The graph is given in the attachment below.
From the figure we can see origin lies on the shaded region.Hence (0,0) should satisfy the inequality.
LHS=y=0
RHS=[tex]-\frac{3x}{2}+1=1\ (x=0)[/tex]
LHS<RHS as 0<1
Hence , the inequality is:
[tex]y<-\frac{3x}{2}+1[/tex]
